Conventional disposable diapers typically have front and back panels which are fastened together around the waist of the newborn infant. However, the still attached umbilical cord of the newborn infant is vulnerable to infection and to frictional irritation by the overlying diaper. The rubbing of the diaper on the umbilical cord when it is still raw can cause inflammation and painful soreness to the infant. The diaper may also trap bacteria at the umbilical site and bring about an infection, particularly when it becomes contaminated with infant feces and urine.